Judging the ‘passability’ of dynamic gaps in a virtual rugby environment

Affordances have recently been proposed as a guiding principle in perception–action research in sport (Fajen, Riley, & Turvey, 2009). In the present study, perception of the ’passability’ affordance of a gap between two approaching defenders in rugby is explored. A simplified rugby gap closure scenario was created using immersive, interactive virtual reality technology where 14 novice participants (attacker) judged the passability of the gap between two virtual defenders via a perceptual judgment (button press) task. The scenario was modeled according to tau theory (Lee, 1976) and a psychophysical function was fitted to the response data. Results revealed that a tau-based informational quantity could account for 82% of the variance in the data. Findings suggest that the passability affordance in this case, is defined by this variable and participants were able to use it in order to inform prospective judgments as to passability. These findings contribute to our understanding of affordances and how they may be defined in this particular sporting scenario; however, some limitations regarding methodology, such as decoupling perception and action are also acknowledged.

On the treatment of singularities of the Watson Hamiltonian for nonlinear molecules

The applicability of the Watson Hamiltonian for the description of nonlinear molecules—especially triatomic ones—has always been questioned, as the Jacobian of the transformation that leads to the Watson Hamiltonian, vanishes at the linear configuration. This results in singular behavior of the Watson Hamiltonian, giving rise to serious numerical problems in the computation of vibrational spectra, with unphysical, spurious vibrational states appearing among the physical vibrations, especially in the region of highly excited states. In this work, we analyze the problem and propose a simple way to confine the nuclear wavefunction in such a way that the spurious solutions are eliminated. We study the water molecule and observe an improvement compared with previous results. We also apply the method to the van der Walls molecule XeHe2.